Fundamentals of machine elements

Fundamentals of

Machine Elements

Third Edition

Third

Edition

Steven R. Schmid

Bernard J. Hamrock

Bo O. Jacobson

Schmid

Hamrock

Jacobson

K23633

Mechanical Engineering

Fundamentals of

Machine Elements

New and Improved SI Edition—Uses SI Units Exclusively in the Text SI Version

Adapting to the changing nature of the engineering profession, this third edition of Fundamentals of

Machine Elements aggressively delves into the fundamentals and design of machine elements with an

SI version. This latest edition includes a plethora of pedagogy, providing a greater understanding of

theory and design.

Signicantly Enhanced and Fully Illustrated

The material has been organized to aid students of all levels in design synthesis and analysis

approaches, to provide guidance through design procedures for synthesis issues, and to expose the

reader to a wide variety of machine elements. Each chapter contains a quote and photograph related

to the chapter as well as case studies, examples, design procedures, an abstract, list of symbols and

subscripts, recommended readings, a summary of equations, and end-of-chapter problems.

What’s New in This Edition:

• Covers life cycle engineering

• Provides a description of the hardness and common hardness tests

• Offers an inclusion of flat groove stress concentration factors

• Adds the staircase method for determining endurance limits and includes Haigh diagrams to

show the effects of mean stress

• Discusses typical surface finishes in machine elements and manufacturing processes used

to produce them

• Presents a new treatment of spline, pin, and retaining ring design, and a new section on

the design of shaft couplings

• Reflects the latest International Standards Organization standards

• Simplifies the geometry factors for bevel gears

• Includes a design synthesis approach for worm gears

• Expands the discussion of fasteners and welds

• Discusses the importance of the heat affected zone for weld quality

• Describes the classes of welds and their analysis methods

• Considers gas springs and wave springs

• Contains the latest standards and manufacturer’s recommendations on belt design, chains,

and wire ropes

The text also expands the appendices to include a wide variety of material properties, geometry

factors for fracture analysis, and new summaries of beam deflection.

SI Version

Fundamentals of Machine Elements SI Version

Third Edition

Fundamentals of

Machine Elements

Third Edition

SI Version

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CRC Press is an imprint of the

Taylor & Francis Group, an informa business

Boca Raton London New York

Fundamentals of

Machine Elements

Steven R. Schmid

Bernard J. Hamrock

Bo O. Jacobson

Third Edition

SI Version

K23633_FM.indd 3 5/21/14 2:30 PM

CRC Press

Taylor & Francis Group

6000 Broken Sound Parkway NW, Suite 300

Boca Raton, FL 33487-2742

© 2014 by Taylor & Francis Group, LLC

CRC Press is an imprint of Taylor & Francis Group, an Informa business

No claim to original U.S. Government works

Version Date: 20140501

International Standard Book Number-13: 978-1-4822-4750-3 (eBook - PDF)

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Dedication

This book is dedicated to Professor Bernard J. Hamrock, a great friend and mentor. Those who have had the pleasure of knowing

him understand that his is a rare intellect: a world-class researcher who fundamentally changed machine design with his con￾tributions to contact mechanics and lubrication theory; a gifted instructor and research advisor; a prolific author of exceptional

papers and books; and a valuable colleague to all who have come to know him.

Professor Hamrock’s professional accomplishments are exceeded only by his personal ones: A beloved husband, his love

for his wife, Rosemary, is unwavering, as is his dedication as a father and grandfather; friendly to all, and a trusted friend

when needed. He is by no means the stereotypical bookish professor. A football athlete in his youth, he maintains a love of the

Buckeyes, of his world travels and his wine sommeliering. Those who know Bernie are grateful for the experience.

Steven R. Schmid

Notre Dame, Indiana

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vii

Contents

Part I — Fundamentals

1. Introduction

1.1 What is Design? 4

1.2 Design of Mechanical Systems 4

1.3 Design as a Multidisciplinary Endeavor 5

1.4 Design of Machine Elements 6

1.5 Computers in Design 12

1.6 Catalogs and Vendors 13

1.7 Units 13

1.8 Unit Checks 14

1.9 Significant Figures 15

1.10 Summary 16

2. Load, Stress, and Strain

2.1 Introduction 22

2.2 Critical Section 22

2.3 Load Classification and Sign Convention 23

2.4 Support Reactions 24

2.5 Static Equilibrium 24

2.6 Free-Body Diagram 26

2.7 Supported Beams 27

2.8 Shear and Moment Diagrams 27

2.9 Stress 34

2.10 Stress Element 34

2.11 Stress Tensor 35

2.12 Plane Stress 35

2.13 Mohr’s Circle 37

2.14 Three-Dimensional Stresses 39

2.15 Octahedral Stresses 40

2.16 Strain 41

2.17 Strain Tensor 42

2.18 Plane Strain 42

2.19 Summary 44

3. Introduction to Materials and Manufacturing

3.1 Introduction 54

3.2 Ductile and Brittle Materials 54

3.3 Classification of Solid Materials 55

3.4 Stress-Strain Diagrams 58

3.5 Properties of Solid Materials 60

3.6 Stress-Strain Relationships 67

3.7 Two-Parameter Materials Charts 68

3.8 Effects of Manufacturing 74

3.9 Summary 83

4. Stresses and Strains

4.1 Introduction 90

4.2 Properties of Beam Cross Sections 90

4.3 Normal Stress and Strain 94

4.4 Torsion 98

4.5 Bending Stress and Strain 99

4.6 Transverse Shear Stress and Strain 104

4.7 Summary 109

5. Deformation

5.1 Introduction 116

5.2 Moment-Curvature Relation 116

5.3 Singularity Functions 117

5.4 Method of Superposition 120

5.5 Strain Energy 120

5.6 Castigliano’s Theorem 123

5.7 Summary 126

viii

6. Failure Prediction for Static Loading

6.1 Introduction 134

6.2 Stress Concentration 134

6.3 Fracture Mechanics 140

6.4 Modes of Crack Growth 141

6.5 Fracture Toughness 141

6.6 Failure Prediction for Uniaxial Stress State 143

6.7 Failure Prediction for Multiaxial Stress State 144

6.8 Summary 152

7. Fatigue and Impact

7.1 Introduction 160

7.2 Fatigue 160

7.3 Cyclic Stresses 162

7.4 Strain Life Theory of Fatigue 162

7.5 Fatigue Strength 163

7.6 Fatigue Regimes 168

7.7 Stress Concentration Effects 169

7.8 The Modified Endurance Limit 171

7.9 Cumulative Damage 175

7.10 Influence of Nonzero Mean Stress 176

7.11 Influence of Multi-Axial Stress States 180

7.12 Fracture Mechanics Approach to Fatigue 182

7.13 Linear Impact Stresses and Deformations 183

7.14 Summary 186

8. Lubrication, Friction, and Wear

8.1 Introduction 196

8.2 Surface Parameters 196

8.3 Conformal and Nonconformal Surfaces 197

8.4 Hertzian Contact 198

8.5 Bearing Materials 203

8.6 Lubricant Rheology 205

8.7 Regimes of Lubrication 211

8.8 Friction 214

8.9 Wear 216

8.10 Summary 220

Part II — Machine Elements

9. Columns

9.1 Introduction 228

9.2 Equilibrium Regimes 228

9.3 Concentrically Loaded Columns 229

9.4 End Conditions 231

9.5 Euler’s Buckling Criterion 232

9.6 Johnson’s Buckling Criterion 232

9.7 AISC Criteria 234

9.8 Eccentrically Loaded Columns 234

9.9 Summary 238

10. Stresses and Deformations in Cylinders

10.1 Introduction 244

10.2 Tolerances and Fits 244

10.3 Pressurization Effects 245

10.4 Rotational Effects 250

10.5 Press Fits 252

10.6 Shrink Fits 254

10.7 Summary 256

ix

11. Shafting and Associated Parts

11.1 Introduction 264

11.2 Design of Shafts for Static Loading 264

11.3 Fatigue Design of Shafts 267

11.4 Additional Shaft Design Considerations 271

11.5 Critical Speed of Rotating Shafts 272

11.6 Keys, Roll Pins, Splines and Set Screws 275

11.7 Retaining Rings and Pins 278

11.8 Flywheels 279

11.9 Couplings 285

11.10 Summary 288

12. Hydrodynamic and Hydrostatic Bearings

12.1 Introduction 298

12.2 The Reynolds Equation 299

12.3 Thrust Slider Bearings 303

12.4 Journal Slider Bearings 314

12.5 Squeeze Film Bearings 321

12.6 Hydrostatic Bearings 322

12.7 Summary 327

13. Rolling-Element Bearings

13.1 Introduction 337

13.2 Historical Overview 337

13.3 Bearing Types and Selection 338

13.4 Geometry 341

13.5 Kinematics 346

13.6 Separators 348

13.7 Static Load Distribution 349

13.8 Elastohydrodynamic Lubrication 359

13.9 Fatigue Life 361

13.10 Variable Loading 367

13.11 Summary 369

14. General Gear Theory; Spur Gears

14.1 Introduction 380

14.2 Types of Gears 380

14.3 Gear Geometry 381

14.4 Gear Ratio 386

14.5 Contact Ratio and Gear Velocity 387

14.6 Tooth Thickness and Backlash 389

14.7 Gear Trains 390

14.8 Gear Manufacture and Quality 392

14.9 Gear Materials 395

14.10 Loads Acting on a Gear Tooth 400

14.11 Bending Stresses in Gear Teeth 400

14.12 Contact Stresses in Gear Teeth 406

14.13 Elastohydrodynamic Film Thickness 407

14.14 Gear Design Synthesis 409

14.15 Summary 412

15. Helical, Bevel, and Worm Gears

15.1 Introduction 422

15.2 Helical Gears 422

15.3 Bevel Gears 427

15.4 Worm Gears 436

15.5 Summary 442

x

16. Fasteners, Connections, and Power Screws

16.1 Introduction 448

16.2 Thread Terminology, Classification, and Designation 448

16.3 Power Screws 450

16.4 Threaded Fasteners 454

16.5 Riveted Fasteners 464

16.6 Welded, Brazed, and Soldered Joints 467

16.7 Adhesive Bonding 474

16.8 Integrated Snap Fasteners 476

16.9 Summary 479

17. Springs

17.1 Introduction 492

17.2 Spring Materials 492

17.3 Helical Compression Springs 495

17.4 Helical Extension Springs 502

17.5 Helical Torsion Springs 504

17.6 Leaf Springs 506

17.7 Gas Springs 508

17.8 Belleville Springs 509

17.9 Wave Springs 509

17.10 Summary 512

18. Brakes and Clutches

18.1 Introduction 520

18.2 Thermal Considerations 520

18.3 Thrust Pad Clutches and Brakes 522

18.4 Cone Clutches and Brakes 525

18.5 Block or Short-Shoe Brakes 526

18.6 Long-Shoe, Internal, Expanding Rim Brakes 528

18.7 Long-Shoe, External, Contracting Rim Brakes 532

18.8 Symmetrically Loaded Pivot-Shoe Brakes 533

18.9 Band Brakes 535

18.10 Slip Clutches 536

18.11 Summary 538

19. Flexible Machine Elements

19.1 Introduction 548

19.2 Flat Belts 548

19.3 Synchronous Belts 551

19.4 V-Belts 551

19.5 Wire Ropes 555

19.6 Rolling Chains 559

19.7 Summary 566

Appendix A: Physical and Mechanical Properties of Materials 573

Appendix B: Stress-Strain Relationships 583

Appendix C: Stress Intensity Factors for Some Common Crack Geometries 591

Appendix D: Shear, Moment, and Deflection of Selected Beams 597

Appendix E: Dimensions of Threaded Fasteners 601

Index 605

xi

Preface

The nature of the engineering profession is changing. It

was once commonplace that students had significant machin￾ery exposure before studying mechanical engineering, and it

always was assumed that students would receive practical

experience in internships or some form of co-operative em￾ployment during their college years, if not sooner. Students

were historically drawn from much less diverse groups than

today; students from a few decades ago (such as the authors)

naturally gained experience with machinery from working

on their car or tractor, and this experience was especially

helpful for courses in design of machine elements. The de￾mographics have changed, permanently and irrevocably, and

the characteristics of incoming students have also changed.

This has been exacerbated by the advances in technology that

make maintenance of most machinery a discipline for only

the specially trained. However, with a broad perspective, it

has become clear that the demographics change has been an

extremely positive development for the profession.

Design presents a number of challenges and opportuni￾ties to instructors. As a topic of study it is exciting because

of its breadth and unending ability to provide fascinating op￾portunities for research, analysis, and creativity. Literally ev￾ery discipline and sub-discipline in engineering has strong

ties to design, and most universities have used design and

manufacturing as the basis of a capstone course that culmi￾nates a mechanical engineering bachelor’s degree. To stu￾dents of engineering, it is, at first, an intimidating field so

enormous that any semester or academic year sequence in

machine design can do nothing but scratch the surface of the

subject. This perception is absolutely true; like so many other

areas of specialization within engineering, design truly is an

area where lifelong learning is necessary.

Machine design is a challenge to both instructors and

students. There are a number of courses, such as statics,

dynamics, solid and fluid mechanics, etc., where topics for

study are broken down into small portions and where closed￾form, quantitative problems are routinely solved by students

and by faculty during lectures. Such problems are important

for learning concepts, and they give students a sense of se￾curity in that absolute answers can be determined. Too of￾ten, machine design is presented in a similar fashion. While,

in practice, such closed-form solutions do exist, they are rel￾atively rare. Usually, multiple disciplines are blended, and

the information available is insufficient to truly optimize a

desired outcome. In practice, engineers need to apply good

judgment after they have researched a problem as best they

can, given budgetary and time restrictions. They must then

state or decide upon a solution, if not an answer. These dif￾ficult open-ended problems are much more demanding than

closed-form solutions, and require a different mindset. In￾stead of considering a number as valid or invalid (usually

by checking against the answer provided in the book or by

the instructor), an open-ended problem can be evaluated only

with respect to whether the result is reasonable and if good

scientific methods were used. As experimental philosophers,

design engineers should not hesitate proving their designs

with prototypes or demonstrations. Of course, many stu￾dents are taught that three weeks of modeling can save a day

in the laboratory. (Sadly, this statement is not always recog￾nized as ironic.)

This book is intended to provide the undergraduate stu￾dent with a clear and thorough understanding of both the

theory and application of the fundamentals of machine ele￾ments. It is expected that this book will also be used as a

reference by practicing engineers. The book is not directed to￾ward lower level undergraduate students — familiarity with

differential and integral calculus is often needed to compre￾hend the material presented. The design of machine elements

involves a great deal of geometry as well. Therefore, the abil￾ity to sketch the various configurations that arise, as well as

to draw a free-body diagram of the loads acting on a com￾ponent, are also needed. The material covered in this text

is appropriate as a third- or fourth-year engineering course

for students who have studied basic engineering sciences, in￾cluding physics, engineering mechanics, and materials and

manufacturing processes.

The book is divided into two parts. Part I (Chapters 1

to 8) presents the fundamentals, and Part II (Chapters 9 to

19) uses the fundamentals in considering the design of var￾ious machine elements. The material in Part I is sequential;

material presented in early chapters is needed in subsequent

chapters. This building-block approach provides the founda￾tion necessary to design the various machine elements con￾sidered in Part II.

Learning Tools

The following pedagogical devices are used in each chapter

to improve understanding and motivate the student:

• Each chapter will open with a photograph that clearly

depicts the machine elements or topics covered in the

chapter. Chapters will also have an opening quotation

that is related to the chapter; the goal is to pique the

reader’s interest in the subject matter and start each

chapter with a positive and entertaining feature to draw

the students into the topic.

• In the margin to the side of the illustration, the contents,

examples, case studies, and design procedures present

in the chapter are listed.

• After the illustration, each chapter has a brief abstract

that indicates the contents at a very high level. Part of

this abstract will include a list of machine elements cov￾ered in the chapter, the typical applications of the ma￾chine elements in the chapter, and the alternate machine

elements that can be considered by designers.

• A list of symbols and subscripts is then presented to help

students with nomenclature as they read the chapter.

• Figures and tables have been redrawn in this edition to

use modern graphical procedures of three-dimensional

sketches, thick boundary lines, and sans-serif fonts in

illustrations.

• Examples are printed with a light gray background to

differentiate them from the text. Examples demonstrate

the mathematical procedures covered and are useful for

students performing quantitative problems.

• Design procedures are printed with a light color back￾ground to differentiate them from the text and exam￾ples. The design procedures are useful guides to com￾mon design problems and aide students with all levels

of Bloom’s taxonomy of learning.

xii

• Case studies are printed with a light color background

and are placed just before the chapter-ending summary.

Case studies are mostly qualitative descriptions of im￾portant modern applications of the chapter’s machine

elements, but at a depth that requires an understand￾ing of the chapter material. Case studies are intended

to reference the chapter’s subject matter and place it in

the proper design framework so that students have no

doubt that the chapter is relevant and important.

• After the summary, the chapter has a list of key words

that the student can use for study or to help with jargon

when necessary.

• A summary of equations is contained after the key

words, and is intended to help students as they work on

chapter-ending problems. The summary of equations is

also a useful handout for instructors to copy and give to

the students for exams.

• Every chapter includes lists of recommended readings

consisting of modern as well as classic books and other

resources that are especially timeless and relevant.

• The styles of the chapter-ending problems have been

designed to cover every stage in modern learning tax￾onomies. Chapter-ending problems are organized as:

1. Questions. These address the “remembering” task

of learning taxonomies.

2. Qualitative Problems. These are carefully de￾signed to take an understanding of machine ele￾ments gleaned from the book and lecture and ap￾plying them to a new situation.

3. Quantitative Problems. These problems focus on

numerical analysis, with some extension to eval￾uating designs and results. Historically, machine

element texts have provided only such analysis

problems. Answers to the majority of quantitative

problems are given. Solutions to the homework

problems can be found in the Instructor’s Solu￾tions Manual, available to instructors who adopt

the text. In addition, most problems have work￾sheets, where a partial solution is provided.

4. Synthesis, Design, and Projects. These are open￾ended, often team-based exercises that require cre￾ation of new designs or principles and that go be￾yond normal analysis problems.

Engineering educators will recognize that the end-of￾chapter problems are designed to accommodate taxonomies

of learning, allowing students of all backgrounds to develop

an understanding, familiarity, and mastery of the subject mat￾ter.

The qualitative problems and synthesis, design, and

projects class of problems also promote a useful method of

active learning. In addition to conventional lecture format

classes, an instructor can incorporate these problems in “sem￾inar” sessions, active learning, or else for group projects. The

authors have found this approach to be very useful and ap￾preciated by students.

Certain users will recognize a consistent approach and

pedagogy as the textbook Manufacturing Engineering and Tech￾nology, and will find that the texts complement each other.

This is by intent, and it is hoped that the engineering student

will realize quickly that to do manufacturing or design, one needs

to know both.

Web Site

A web site containing other book-related resources can be

found at www.crcpress.com/product/isbn/9781482247480.

The web site provides reported errata, web links to related

sites of interest, password-protected solutions to homework

problems for instructors, a bulletin board, and information

about ordering books and supplements. The web site also

contains presentation files for instructors and students, using

full-color graphics whenever possible.

Contents

Chapter 1 introduces machine design and machine elements

and covers a number of topics, such as safety factors, statis￾tics, units, unit checks, and significant figures. In designing

a machine element it is important to evaluate the kinemat￾ics, loads, and stresses at the critical section. Chapter 2 de￾scribes the applied loads (normal, torsional, bending, and

transverse shear) acting on a machine element with respect

to time, the area over which the load is applied, and the loca￾tion and method of application. The importance of support

reaction, application of static force and moment equilibrium,

and proper use of free-body diagrams is highlighted. Shear

and moment diagrams applied to beams for various types of

singularity function are also considered. Chapter 2 then de￾scribes stress and strain separately.

Chapter 3 focuses on the properties of solid engineer￾ing materials, such as the modulus of elasticity. (Appendix

A gives properties of ferrous and nonferrous metals, ceram￾ics, polymers, and natural rubbers. Appendix B explores the

stress-strain relationships for uniaxial, biaxial, and triaxial

stress states.) Chapter 4 describes the stresses and strains that

result from the types of load described in Chapter 2, while

making use of the general Hooke’s law relationship devel￾oped in Appendix B. Chapter 4 also considers straight and

curved members under these four types of load.

Certainly, ensuring that the design stress is less than

the yield stress for ductile materials and less than the ulti￾mate stress for brittle materials is important for a safe design.

However, attention must also be paid to displacement (defor￾mation) since a machine element can fail by excessive elastic

deformation. Chapter 5 attempts to quantify the deformation

that might occur in a variety of machine elements. Some ap￾proaches investigated are the integral method, the singularity

function, the method of superposition, and Castigliano’s the￾orem. These methods are applicable for distributed loads.

Stress raisers, stress concentrations, and stress concen￾tration factors are investigated in Chapter 6. An impor￾tant cause of machine element failure is cracks within the

microstructure. Therefore, Chapter 6 covers stress levels,

crack-producing flaws, and crack propagation mechanisms

and also presents failure prediction theories for both uniaxial

and multiaxial stress states. The loading throughout Chap￾ter 6 is assumed to be static (i.e., load is gradually applied

and equilibrium is reached in a relatively short time). How￾ever, most machine element failures involve loading condi￾tions that fluctuate with time. Fluctuating loads induce fluc￾tuating stresses that often result in failure by means of cumu￾lative damage. These topics, along with impact loading, are

considered in Chapter 7.

Chapter 8 covers lubrication, friction, and wear. Not

only must the design stress be less than the allowable stress

and the deformation not exceed some maximum value, but

also lubrication, friction, and wear (tribological considera￾tions) must be properly understood for machine elements to

be successfully designed. Stresses and deformations for con-

xiii

centrated loads, such as those that occur in rolling-element

bearings and gears, are also determined in Chapter 8. Simple

expressions are developed for the deformation at the center

of the contact as well as for the maximum stress. Chapter 8

also describes the properties of fluid film lubricants used in

a number of machine elements. Viscosity is an important pa￾rameter for establishing the load-carrying capacity and per￾formance of fluid-film lubricated machine elements. Fluid

viscosity is greatly affected by temperature, pressure, and

shear rate. Chapter 8 considers not only lubricant viscosity,

but also pour point and oxidation stability, greases and gases,

and oils.

Part II (Chapters 9 to 20) relates the fundamentals to

various machine elements. Chapter 9 deals with columns,

which receive special consideration because yielding and ex￾cessive deformation do not accurately predict the failure of

long columns. Because of their shape (length much larger

than radius) columns tend to deform laterally upon loading,

and if deflection becomes critical, they fail catastrophically.

Chapter 9 establishes failure criteria for concentrically and ec￾centrically loaded columns.

Chapter 10 considers cylinders, which are used in many

engineering applications. The chapter covers tolerancing of

cylinders; stresses and deformations of thin-walled, thick￾walled, internally pressurized, externally pressurized, and

rotating cylinders; and press and shrink fits.

Chapter 11 considers shafting and associated parts, such

as keys, snap rings, flywheels, and couplings. A shaft design

procedure is applied to static and cyclic loading; thus, the

material presented in Chapters 6 and 7 is directly applied to

shafting. Chapter 11 also considers critical speeds of rotating

shafts.

Chapter 12 presents the design of hydrodynamic bear￾ings — both thrust and journal configurations — as well as

design procedures for the two most commonly used slider

bearings. The procedures provide an optimum pad config￾uration and describe performance parameters, such as nor￾mal applied load, coefficient of friction, power loss, and lu￾bricant flow through the bearing. Similar design information

is given for plain and nonplain journal bearings. The chapter

also considers squeeze film and hydrostatic bearings, which

use different pressure-generating mechanisms.

Rolling-element bearings are presented in Chapter 13.

Statically loaded radial, thrust, and preloaded bearings are

considered, as well as loaded and lubricated rolling-element

bearings, fatigue life, and dynamic analysis. The use of

the elastohydrodynamic lubrication film thickness is inte￾grated with the rolling-element bearing ideas developed in

this chapter.

Chapter 14 covers general gear theory and the design of

spur gears. Stress failures are also considered. The trans￾mitted load is used to establish the design bending stress

in a gear tooth, which is then compared with an allowable

stress to establish whether failure will occur. Chapter 14 also

considers fatigue failures. The Hertzian contact stress with

modification factors is used to establish the design stress,

which is then compared with an allowable stress to deter￾mine whether fatigue failure will occur. If an adequate pro￾tective elastohydrodynamic lubrication film exists, gear life is

greatly extended.

Chapter 15 extends the discussion of gears beyond spur

gears as addressed in Chapter 14 to include helical, bevel, and

worm gears. Advantages and disadvantages of the various

types of gears are presented.

Chapter 16 covers threaded, riveted, welded, and ad￾hesive joining of members, as well as power screws. Riv￾eted and threaded fasteners in shear are treated alike in de￾sign and failure analysis. Four failure modes are presented:

bending of member, shear of rivet, tensile failure of member,

and compressive bearing failure. Fillet welds are highlighted,

since they are the most frequently used type of weld. A brief

stress analysis for lap and scarf adhesively bonded joints is

also given.

Chapter 17 treats the design of springs, especially helical

compression springs. Because spring loading is most often

continuously fluctuating, Chapter 16 considers the design al￾lowance that must be made for fatigue and stress concentra￾tion. Helical extension springs are also covered in Chapter

16. The chapter ends with a discussion of torsional and leaf

springs.

Brakes and clutches are covered in Chapter 18. The brake

analysis focuses on the actuating force, the torque transmit￾ted, and the reaction forces in the hinge pin. Two theories

relating to clutches are studied: the uniform pressure model

and the uniform wear model.

Chapter 19 deals with flexible machine elements. Flat

belts and V-belts, ropes, and chains are covered. Methods

of effectively transferring power from one shaft to another

while using belts, ropes, and chains are also presented. Fail￾ure modes of these flexible machine elements are considered.

What’s New in This Edition

This third edition represents a major revision from the sec￾ond edition. In addition to the pedagogy enhancements men￾tioned above, the contents have been greatly expanded and

organized to aide students of all levels in design synthe￾sis and analysis approaches. Design synthesis is generally

taught or expected of students only after a machine elements

course in most college curricula. This book attempts to pro￾vide guidance through design procedures for synthesis is￾sues, but it also exposes the reader to a wide variety of ma￾chine elements.

Users of the second edition will immediately recognize

that this third edition has been completely re-typeset using a

space-saving, two-column approach, and all figures redrawn

to match the new column widths. The space-saving typeset￾ting format has saved over 300 pages from the previous edi￾tion, while the content has been expanded considerably. This

was, in fact, a goal: too many textbooks are difficult to use

because they give the impression of completeness, but this is

often illusory. Large margins and gaps between topics arti￾ficially produce heavy tomes. Our goal was to create a book

with good coverage that can be more easily carried by stu￾dents.

In every chapter opening box, the reader is directed to￾ward other machine elements that can serve the same pur￾pose, which can also help in synthesis. As an example, a

student designing a gear set for power transmission between

two shafts may thus be reminded that a belt drive is perhaps

an alternative worthy of consideration.

The book has been designed to compliment the well￾known manufacturing textbooks Manufacturing Processes for

Engineering Materials and Manufacturing Engineering and Tech￾nology by Kalpakjian and Schmid. Students who use both

texts in their engineering studies will recognize similarities

in organization, graphical styles, and, it is hoped, clarity.

The classes of chapter-ending problems have been in￾troduced above, but they have been carefully designed to

aid students to develop a deep understanding of each chap￾ter’s subject matter. They have been developed using learn￾ing taxonomies that require ever-sophisticated cognitive ef￾fort. That is, students are required to remember (Questions),

apply knowledge to fairly simple and straightforward ques￾tions (Qualitative Problems), extend the knowledge to ana-

xiv

lytical problems (Quantitative Problems), and finally asked

to extend their analytical abilities to open-ended and synthe￾sis problems requiring creativity in their solution (Synthesis

and Design Problems).

A major effort has been made to expand coverage in all

areas. Specific changes to this edition include:

• In Chapter 1, additional design considerations have

been listed in Section 1.4, additional examples and case

studies have been added, and life cycle engineering has

been included.

• Chapter 3 now includes a description of hardness and

common hardness tests used for metals; this clarifies the

use of these concepts in gear design. In addition, the

manufacturing discussion has been expanded.

• The use of retaining rings in Chapter 11 necessitated the

inclusion of flat groove stress concentration factors in

Chapter 6.

• Chapter 7, on fatigue design, has been significantly

expanded. The staircase method for determining en￾durance limits has been added in Design Procedure 7.2,

the fatigue strength concentration factor descriptions are

longer with more mathematical models, and Haigh di￾agrams are included to show the effects of mean stress.

Additional material data has been included for the frac￾ture mechanics approaches to fatigue design.

• In Chapter 8, a streamlined discussion of typical surface

finishes in machine elements, and manufacturing pro￾cesses used to produce them, has been prepared. In ad￾dition, a discussion of the commonly used bearing ma￾terials has been added.

• Chapter 11 has been expanded considerably. In addi￾tion to an expanded discussion of keys and set screws,

the chapter presents new treatment of spline, pin, and

retaining ring design, and has a new section on the de￾sign of shaft couplings.

• Hydrodynamic bearings are increasingly important be￾cause of their widespread use in transportation and

power industries; while the discussion of thrust and

journal bearings has been retained, the analysis is sim￾plified and more straightforward. The discussion of

squeeze film and hydrostatic bearings has been ex￾panded.

• Chapter 13 has been extensively rewritten to reflect the

latest International Standards Organization standards

that unify the approach used to design rolling element

bearings. This has allowed a simplification of bearing

selection and analysis, as will be readily apparent. Fur￾ther, this remains the only machine element book that

accurately depicts the wide variety of bearings avail￾able. This treatment now includes the topic of toroidal

bearings, a novel design that is now widely available,

and leads to compact and high load carrying designs.

Life adjustment factors and effects of variable loading

have been expanded, and an industrially relevant case

study on windmill bearings has been exhaustively re￾searched and included in the chapter.

• The treatment of spur gear design in Chapter 14 has

been modified to reflect the latest advances in materi￾als, including powder metal materials that have become

extremely popular for automotive applications. The im￾portance of lubrication in gears has been emphasized.

Further, a design synthesis approach for spur gear de￾sign has been included in Section 14.14.

• Geometry factors for bevel gears in Chapter 15 have

been simplified without loss in accuracy. Also, a design

synthesis approach for worm gears has been included.

• The discussion of fasteners and welds in Chapter 16

has been expanded considerably. The importance of the

heat affected zone for weld quality is discussed, and

the classes of welds and their analysis methods are de￾scribed. This includes the treatment of modern welding

approaches such as friction stir welding as well as laser

and electron beam welding.

• Gas springs and wave springs have been added to the

discussion of Chapter 17.

• Chapter 18 has been reorganized, starting with funda￾mental principles that apply to all brake and clutch sys￾tems, especially thermal effects. Additional automotive

examples have been added.

• Chapter 19 has been essentially rewritten to reflect the

latest standards and manufacturer’s recommendations

on belt design, chains, and wire ropes. In addition, silent

chains have been included into the chain discussion.

• The appendices have been expanded to provide the stu￾dent with a wide variety of material properties, geome￾try factors for fracture analysis, and new summaries of

beam deflection. While it is recognized that modern stu￾dents have such information readily available via the In￾ternet, making such material available in the textbook is

useful for reference purposes.

This text has been under preparation for over four years,

and required meticulous efforts at maintaining a consistent

approach, careful statement of design procedures wherever

they were useful, and expansion of chapter-ending problems.

We hope the student of machine element design will enjoy

and benefit from this text.

Steven R. Schmid

The University of Notre Dame

Bernard J. Hamrock

The Ohio State University

Bo O. Jacobson

Lund University